Question: Simplify the following expression: $k = \dfrac{-56r^2 + 72r}{64r^2 - 48r}$ You can assume $r \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-56r^2 + 72r = - (2\cdot2\cdot2\cdot7 \cdot r \cdot r) + (2\cdot2\cdot2\cdot3\cdot3 \cdot r)$ The denominator can be factored: $64r^2 - 48r = (2\cdot2\cdot2\cdot2\cdot2\cdot2 \cdot r \cdot r) - (2\cdot2\cdot2\cdot2\cdot3 \cdot r)$ The greatest common factor of all the terms is $8r$ Factoring out $8r$ gives us: $k = \dfrac{(8r)(-7r + 9)}{(8r)(8r - 6)}$ Dividing both the numerator and denominator by $8r$ gives: $k = \dfrac{-7r + 9}{8r - 6}$